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Class 10MathematicsQuadratic EquationsRoots of a Quadratic EquationHardLevel 32
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If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-9x+18=0\), what is the value of \((\alpha-2)(\beta-2)\)?

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Answer and explanation

Correct answer: 4

By Vieta’s formulas, \(\alpha+\beta=9\) and \(\alpha\beta=18\). Therefore, \((\alpha-2)(\beta-2)=\alpha\beta-2(\alpha+\beta)+4=18-18+4=4\). Hence, option A is correct. Exam tip: 18 is only the product \(\alpha\beta\); the required expression also involves the sum of the roots.

Related tags

Quadratic EquationsRoots Of A Quadratic EquationVieta FormulasTransformed RootsAlgebraic Expressions

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

By Vieta’s formulas, \(\alpha+\beta=9\) and \(\alpha\beta=18\). Therefore, \((\alpha-2)(\beta-2)=\alpha\beta-2(\alpha+\beta)+4=18-18+4=4\). Hence, option A is correct. Exam tip: 18 is only the product \(\alpha\beta\); the required expression also involves the sum of the roots.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.

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